For nearly seven decades, the field of cognitive research has been engaged in a significant internal debate, often described as a civil war. This conflict pits two fundamentally different perspectives against each other: computationalism and connectionism.

Computationalism posits that intelligence is best understood through the lens of rules, symbols, and logic, all of which can be articulated as mathematical equations. In contrast, connectionism proposes that intelligence arises organically from vast, interconnected networks. These networks are modeled on the biological structure of the brain’s neurons, where no single component is inherently intelligent, but the system as a whole exhibits emergent intelligent behavior.

This long-standing intellectual battle has profoundly influenced not only cognitive science but also the development of artificial intelligence, a field now actively reshaping the global economy.

This month, two new books enter this ongoing discourse, each representing a distinct viewpoint from opposing sides of the debate.

Among these, “The Laws of Thought: The Quest for a Mathematical Theory of the Mind” by Princeton professor Tom Griffiths stands out. Griffiths meticulously traces the historical endeavor to formalize human thinking through mathematical laws. His work offers crucial insights into the underpinnings of modern artificial intelligence and speculates on its potential future trajectory.

Griffiths structures his narrative around three distinct, yet increasingly intertwined, mathematical approaches to formalizing thought: rules and symbols, neural networks, and probability. The initial approach, rules and symbols, conceptualizes thinking as a form of problem-solving. This involves breaking down a task into discrete goals and sub-goals, then navigating them through a series of formal steps. This paradigm powered early AI systems.

However, this symbolic approach also highlighted the inherent difficulty in capturing human common sense systematically. The sheer volume of rules required for AI to operate often grew exponentially, quickly escalating into tens of millions of explicit requirements.

Neural networks, conversely, eschew explicit rules in favor of learning from examples. They construct intelligence by integrating numerous simple units. The complex behavior that characterizes intelligence emerges from the intricate interactions among these units. This mirrors, to a degree, how humans operate.

Probability and statistics introduce a crucial third element: uncertainty. Human minds do not possess access to perfect information. A key aspect of human intelligence, according to this perspective, lies in how individuals weigh evidence and update their beliefs in the face of incomplete data.

Griffiths argues that none of these three frameworks, in isolation, is sufficient to fully explain intelligence. He contends that realistic models of intelligence, whether applied to humans or machines, must integrate all three components.

He builds his case through a historical examination of humanity’s attempts to map the mind’s processes using mathematical tools. Griffiths draws upon archival research and interviews with leading researchers in the field. As a result, his book is both detailed and captivating, though at times it can feel somewhat densely written.

A different perspective is presented in “The Emergent Mind: How Intelligence Arises in People and Machines” by neuroscientist Gaurav Suri and Jay McClelland. Their central argument is that the mind is an emergent property of interacting neuronal networks, whether biological or artificial. These networks, they believe, are capable of generating thoughts, emotions, and decisions.

This book draws significantly on McClelland’s foundational work as a pioneer in connectionism. The two books offer contrasting yet illuminating interpretations of the current generative AI revolution.

For Griffiths, a large language model (LLM) serves as a confirmation of his hybrid vision. While impressive, he notes that these models often “hallucinate” and falter, suggesting that a symbolic layer will likely be necessary to refine their capabilities.

Suri and McClelland, however, view the same LLM as a vindication of their connectionist approach. They express astonishment at the extent of reasoning that has emerged from a network functioning solely on its own interconnected structure.

The challenges with “The Emergent Mind” lie less in its core thesis and more in its presentation. The book’s tone oscillates between informal asides and somewhat awkward phrasing. Explaining complex mathematical and scientific concepts was always going to be demanding. Neither book achieves perfect clarity, though “The Laws of Thought” comes closer by focusing on what AI frameworks can and cannot explain through historical context.

Other Notable Works on Machine Intelligence

A more provocative manifesto is found in “The Emergent Mind,” where the authors foresee no fundamental impediment to the emergence of more autonomous, goal-driven AI systems from purely neural architectures. Consequently, this perspective can sometimes feel less grounded in current realities.

Griffiths’s book, in contrast, leaves the reader with a robust understanding of the conceptual “languages” available for describing thought. It strongly suggests that the future of artificial intelligence will likely be found in the intricate and often “messy” interdependencies between these different frameworks.

This raises the question: could this future signal a resolution to the long-standing division between the two ideological camps?

Additional Recommended Readings:

Algorithms to Live By
by Brian Christian and Tom Griffiths
This work provides an engaging, non-technical exploration of how principles from computer science can illuminate everyday decision-making. It particularly highlights how an algorithmic approach can enhance human choices. Co-authored by Griffiths a decade ago, prior to the major advancements in LLMs like ChatGPT, its insights remain highly relevant.
Rebooting AI
Building Artificial Intelligence We Can Trust
by Gary Marcus and Ernest Davis
This book argues that while current neural networks can be impressive, they are often fragile. It advocates for the development of hybrid systems that leverage the strengths of the traditional rules-and-symbols approach—one of the three mathematical frameworks discussed in Griffiths’s new book.

Chris Stokel-Walker is a technology writer based in Newcastle upon Tyne, UK.